Papers by Steven J. Murdoch

This short paper presents a simple game-theoretic analysis of a late stage of the arms race between a censorious national government and the developers of tools for circumventing that censorship. Keyword blocking, IP-address blocking, and protocol blocking for known circumvention protocols have all been insitituted and then evaded. The circumvention tool is now steganographically masking its traffic so it is indistinguishable from some commonly-used, innocuous cover protocol or protocols; the censor, having no way to unmask this traffic, must either block all use of the cover protocol, or give up.

The game-theoretic question is, how many cover protocols should the circumvention tool implement? Obviously, if there are several protocols, then the tool is resilient as long as not all of them are blocked. On the other hand, implementing more cover protocols requires more development effort, and increases the probability that some of them will be imperfectly mimicked, making the tool detectable. [1] This might seem like an intractable question, but the lovely thing about game theory is it lets you demonstrate that nearly all the fine details of each player’s utility function are irrelevant. The answer: if there’s good reason to believe that protocol X will never be blocked, then the tool should only implement protocol X. Otherwise, it should implement several protocols, based on some assessment of how likely each protocol is to be blocked.

In real life there probably won’t be a clear answer to will protocol X ever be blocked? As the authors themselves point out, the censors can change their minds about that quite abruptly, in response to political conditions. So, in real life several protocols will be needed, and that part of the analysis in this paper is not complete enough to give concrete advice. Specifically, it offers a stable strategy for the Nash equilibrium (that is, neither party can improve their outcome by changing the strategy) but, again, the censors might abruptly change their utility function in response to political conditions, disrupting the equilibrium. (The circumvention tool’s designers are probably philosophically committed to free expression, so their utility function can be assumed to be stable.) This requires an adaptive strategy. The obvious adaptive strategy is for the tool to use only one or two protocols at any given time (using more than one protocol may also improve verisimilitude of the overall traffic being surveilled by the censors) but implement several others, and be able to activate them if one of the others stops working. The catch here is that the change in behavior may itself reveal the tool to the censor. Also, it requires all the engineering effort of implementing multiple protocols, but some fraction of that may go to waste.

The paper also doesn’t consider what happens if the censor is capable of disrupting a protocol in a way that only mildly inconveniences normal users of that protocol, but renders the circumvention tool unusable. (For instance, the censor could be able to remove the steganography without necessarily knowing that it is there. [2]) I think this winds up being equivalent to the censor being able to block that protocol without downside, but I’m not sure.